is a web server that solves the RNA
inverse folding problem, using constraint programming.
Given a target RNA secondary structure, as well as optional
nucleotide constraints, RNAiFold determines all (or a large number of)
RNA sequences, whose minimum free energy structure is the target
structure. See

where we show that computing the page number is NP-complete, and describe
an approximation algorithm as well as an exact solution using constraint
programming (CP). The web server is an implementation of the CP algorithm,
which can compute the optimal page number for large RNAs within seconds --
for example the 23S chain PDB file 1FFK of length 2,922 for the
Haloarcula marismortui ribosome.

is a web server that computes the partition function
and samples structures from the ensemble of locally optimal
secondary structures of a given RNA sequence. Here, a locally optimal
secondary structure is one for which the free energy can not
be lowered by the addition or removal of a single base pair (i.e. a
kinetic trap in unit resolution energetics).
The algorithm is described in
the paper

computes the maximum expected accurate
δ-neighbors of a given RNA secondary structure for a given RNA
sequence. Here, a structure T is a δ-neighbor of a given structure
S, if S can be transformed into T by a minimum number δ of edit
operations, where an edit operation consists of removing or adding a single
base pair (i.e. if the base pair distance between S and T is δ).
The algorithm is described in
the paper

is an implementation of the Wang-Landau non-Boltzmannian
sampling algorithm to approximate the partition function for RNA secondary
structures. It is well-known that Monte-Carlo Boltzmannian sampling can be
used to compute an approximation to the minimum free energy
pseudoknotted structure for a given RNA sequence (allowing all possible
pseudoknots). Since it is also NP-complete to compute the
partition function for pseudoknotted RNA structures, Wang-Landau sampling
can be used to estimate the density of states (from which the partition
function can be computed).
The algorithm is described in the paper

is a web server to compute near-optimal folding pathways between
two given secondary structures for a given RNA sequence. Since this
problem is known to be NP-complete, our main algorithm, RNAtabupath
uses the TABU local search heuristic. The web server
includes both downloadable source code for several algorithms, as well
as a web engine to compute pathways. Intended applications concern
folding pathways for RNA conformational switches.
RNApathfinder and the RNAtabupath algorithm are
described in the paper

is a web server to perform mutational analysis for a given RNA sequence.
Previous methods relied on exhaustively enumerating k-point mutant
sequences and subsequently applying mfold or RNAfold, a procedure with
run time exponential in k. In contrast, RNAmutants computes the
minimum free energy structure and Boltzmann partition function for all
k-point mutants, for 0 ≤ k ≤ K, with run time
O(K2n3). RNAmutants is described in the paper

RNAmutants is software to predict
the expected energy of k-point mutants of a given RNA sequence, and
as well to compute the k-superoptimal secondary
structure, or secondary structure whose free energy is a minimum over
all pointwise mutants of a given RNA involving at most k mutated sites.
The algorithms are described in
Energy landscape of k-point mutants of an RNA molecule by
P. Clote, J. Waldispuhl, B. Behzadi, J.-M. Steyaert,
Bioinformatics, Vol. 21, 4140-4147, 2005.

Dishuffle is a web
interface to a local implementation of the Altschul-Erikson
dinucleotide shuffle algorithm, described in
"Significance of nucleotide sequence alignments: A method for random
sequence permutation that preserves dinucleotide and codon usage",
S.F. Altschul and B.W. Erikson,
Mol. Biol. Evol., 2(6):526--538, 1985. This algorithm was used
in the paper,
Structural RNA has lower folding energy than random RNA of the
same dinucleotide frequency, by
P. Clote, F. Ferre, E. Kranakis, D. Krizanc in
RNA 11(5):578-591 (2005).

Boltzmann Alignment
performs a (local) Smith-Waterman alignment of two input proteins,
then calculates the Boltzmann probability of any two aligned residues,
or residue aligned with gap symbol. This idea was first published in
"Stochastic Pairwise Alignments",
U. Mueckstein, I. L. Hofacker, and P. F. Stadler,
Bioinformatics 18 (suppl) 2002,
though it was later independently discovered and implemented in
April 2003 by P. Clote.
See
"Biologically significant sequence alignments using
Boltzmann probabilities" by P. Clote.